A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$8.50$, and bags of cookies cost $$3.00$, and sales equaled $$55.00$ in total. There were $3$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${8.5x+3y = 55}$ ${y = x+3}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+3}$ for $y$ in the first equation. ${8.5x + 3}{(x+3)}{= 55}$ Simplify and solve for $x$ $ 8.5x+3x + 9 = 55 $ $ 11.5x+9 = 55 $ $ 11.5x = 46 $ $ x = \dfrac{46}{11.5} $ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $ {y = x+3}$ to find $y$ ${y = }{(4)}{ + 3}$ ${y = 7}$ You can also plug ${x = 4}$ into $ {8.5x+3y = 55}$ and get the same answer for $y$ ${8.5}{(4)}{ + 3y = 55}$ ${y = 7}$ $4$ bags of candy and $7$ bags of cookies were sold.